Maximum Principle for the Regularized Schrödinger Operator

In this paper we present analogues of the maximum principle and of some parabolic inequalities for the regularized time-dependent Schrödinger operator on open manifolds using Günter derivatives. Moreover, we study the uniqueness of bounded solutions for the regularized Schrödinger–Günter problem and obtain the corresponding fundamental solution. Furthermore, we present a regularized Schrödinger kernel and prove some convergence results. Finally, we present an explicit construction for the fundamental solution to the Schrödinger–Günter problem on a class of conformally flat cylinders and tori.     

Photophysical properties of binuclear ruthenium(ii) bis(2,2':6',2''-terpyridine) complexes built around a central 2,2'-bipyrimidine receptor

A binuclear complex has been synthesized having ruthenium(ii) bis(2,2':6',2'-terpyridine) terminals attached to a central 2,2'-bipyrimidine unit via ethynylene groups. Cyclic voltammetry indicates that the substituted terpyridine is the most easily reduced subunit and the main chromophore involves charge transfer from the metal centre to this ligand. The resultant metal-to-ligand, charge-transfer (MLCT) triplet state is weakly emissive and has a lifetime of 60 ns in deoxygenated solution at room temperature. The luminescence yield and lifetime increase with decreasing temperature in a manner that indicates the lowest-energy MLCT triplet couples to at least two higher-energy triplets. Cations can bind to the central bipyrimidine unit, forming both 1:1 and 1:2 (ligand:metal) complexes as confirmed by electrospray MS analysis. The photophysical properties depend on the number of bound cations and on the nature of the cation. In the specific case of binding zinc(ii) cations, the 1:1 complex has a triplet lifetime of 8.0 ns while that of the 1:2 complex is 1.8 ns. The 1:1 complexes formed with Ba(2+) and Mg(2+) are more luminescent than is the parent compound while the 1:2 complexes are much less luminescent. It is shown that the coordinated cations raise the reduction potential of the central bipyrimidine unit and thereby increase the activation energy for coupling with the metal-centred state. Complexation also introduces a non-emissive intramolecular charge-transfer (ICT) state that couples to the lowest-energy MLCT triplet and provides an additional non-radiative decay route. The triplet state of the 1:2 complex formed with added Zn(2+) cations decays preferentially via this ICT state.     

Laterally nanostructured adsorbed layers of surfactant/surfmer mixtures before and after polymerisation

The adsorbed layer structure of mixed films of the polymerisable cationic surfactant dodecyldimethyl(ethylmethacrylate)ammonium bromide (MEDDAB) with the cationic and non-ionic surfactants dodecyltrimethylammonium bromide (DTAB) and polyoxyethylene-23-lauryl ether (C12E23) has been investigated by AFM soft-contact imaging before and after solution polymerisation of MEDDAB. MEDDAB alone adsorbs on mica as a planar bilayer, but the adsorbed layer structure can be modified by mixing with DTAB or C12E23 to yield an adsorbed mesh or cylinders. The equilibrium adsorbed film structure after solution polymerisation of the methacrylate group on MEDDAB was found to depend on the solubilising ability of the non-polymerisable surfactant. C12E23 effectively prevented precipitation of polymerised MEDDAB, retaining the unpolymerised adsorbed layer structure, whereas DTAB mixtures became cloudy above 23 mol% MEDDAB. The resultant structure remained similar to the adsorbed rods formed prior to polymerisation, but had a diameter several times larger.     

Solvent-controlled formation of η-butadienyl or η-allyl group 6 transition metal complexes in water or alcohols

Preparation of acyl chloride, ester, amide or thioester-substituted η³-butadienyl complexes of the type [MCl(CO)₂(η³-CH₂C(COXR)CCH₂)(L₂)] (M=Mo,W; XR=Cl, OR, NHR, SR; L₂=1,10-phenanthroline (phen), 2,9-dimethyl-1,10-phenanthroline) from 1,4-dichloro-2-butyne and Ph₄P[MCl(CO)₃(L₂)] in water resulted in improved yields (M=Mo) and recycling of reagents. Whilst analogous reactions in anhydrous methanol to yield either substituted η³-butadienyl (XR=OR) or η³-allyl [MoCl(CO)₂(η³-CH₂C(CO₂R)C(OR)Me)(phen)] were dependent upon the presence of organic bases or ethers, reactions in propanol or butanol gave the η³-butadienyl complexes only. Possible mechanisms are discussed. Halide extraction from ester or amide butadienyl complexes in hydroxylic solvents gave highly reactive cations of the type [Mo(CO)₂(η³-butadienyl)(phen)(solvent]⁺, and carboxylate products were obtained by displacement of metal-bound solvent by glucuronate or hydroxybutyrate ions.